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  • The function <img alt="f\left ( x \right )=log\left ( \frac{1-x}{1+x} \right )" src="/latex-image/?f%5Cleft%20%28%20x%20%5Cright%20%29%3Dlog%5Cleft%20%28%20%5Cfrac%7B1-x%7D%7B1&plus;x%7D%20%5Cr

The function f\left ( x \right )=log\left ( \frac{1-x}{1+x} \right ) is

Option: 1

Even function


Option: 2

Odd function


Option: 3

Neither even nor odd


Option: 4

Can't say


Answers (1)

\begin{aligned} f(-x) &=\log \left(\frac{1-(-x)}{1+(-x)}\right) \\ &=\log \left(\frac{1+x}{1-x}\right) \\ &=\log \left(\left(\frac{1-x}{1+x}\right)^{-1}\right) \\ &=-\log \left(\frac{1-x}{1+x}\right) \\ &=-f(x) \\ \Rightarrow f(-x) &=-f(x) \end{aligned}

So, it is an odd function.

 

Posted by

Kshitij

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